The basic answer is you can only research ONE tech at a time. However, if you have a very large research output applied to a cheap tech, you will produce more research points than that tech requires, and the overflow will be applied to the next tech in line.
Giving random numbers pulled out of my ass to illustrate the point:
Say you have an output of 1000 points, and you are researching Lasers 1, which costs 200 points to research. When Lasers 1 is finished, the remaining 800 points will be applied to Lasers 2, which costs 250 points. The remaining 550 would then be applied to Lasers 3, then Lasers 4, until you run out of research output for that turn. At the end of the turn, you will see three or four techs show up as being researched that turn, even though you were only "officially" allowed to research one tech each turn.
Exceptions to the above: you are limited to reseaching N+1 techs per turn, where N is the number of colonies you own. Very rarely will a beginner run into that problem.
If you run into the end of a line of research (such as the final beam weapon Doom Ray), any research output you have beyond what you need to research that tech is simply lost.
There are other circumstances that can result in getting the research complete screen, such as trading for techs, stealing a tech through espionage or invasion, or a vote from the United Planets that forces tech sharing.
Occasionally, anomalies will give you direct bonus research points, equal to 25% of what you are currently researching. If this results in finishing the tech, you get an opportunity to choose another research topic before the rest of the turn processes. This can result in getting techs from two lines in the same turn, but only because one of them was not due to direct research output.
There are a few other minor bits I'm sure I missed, but those are the highlights and major exceptions.